Solved: In the design of all-terrain vehicles, it is necessary to consider the failure

Chapter 2, Problem 34

(choose chapter or problem)

In the design of all-terrain vehicles, it is necessary to consider the failure of the vehicle when attempting to negotiate two types of obstacles. One type of failure is called hang-up failure and occurs when the vehicle attempts to cross an obstacle that causes the bottom of the vehicle to touch the ground. The other type of failure is called nose-in failure and occurs when the vehicle descends into a ditch and its nose touches the ground. The accompanying figure, adapted from [Bek], shows the components associated with the nosein failure of a vehicle. In that reference it is shown that the maximum angle that can be negotiated by a vehicle when is the maximum angle at which hang-up failure does not occur satisfies the equation A sin cos + B sin2 C cos E sin = 0, where A = l sin 1, B = l cos 1, C = (h + 0.5D)sin 1 0.5D tan 1, and E = (h + 0.5D) cos 1 0.5D. a. It is stated that when l = 89 in., h = 49 in., D = 55 in., and 1 = 11.5, angle is approximately 33. Verify this result. b. Find for the situation when l, h, and 1 are the same as in part (a) but D = 30 in.